Ellis,J. Pressure transients in water engineering, A guide to analysis and interpretation of behaviour
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where Q
out
is an average over the time step, or
A
s
ðH H
o
Þ=t ¼ðV þ V
o
ÞA
p
=2 Q
out
where suffix ‘o’ denotes conditions at the beginning of the time incre-
ment t. Eliminating V using the quasi-invariant equation:
A
s
ðH H
o
Þ=t ¼ðJþg=aH þ V
o
ÞA
p
=2 Q
out
ð16:4Þ
which is easily solved for piezometric level H. By substitution in the
quasi-invariant equation, V is found.
Under reversed flow it is also possible to drain a small chamber with
the consequence that discharge head is lowered to the inlet pipe level
and an air pocket can penetrate the upstream pipeline as with the
vertical bellmouth outlet.
16.3 Back-flow connection
The possibility of significant head drop at the downstream end of a
pipeline due to reversed flow has been highlighted in considering
discharge conditions of sections 16.1 and 16.2. In a treated water
system, the amount of reversed flow may be sufficient to draw down
piezometric level to the point where pressures in the pipeline become
too low. A back-flow connection may allow reversed flow without
unacceptable pressure drop. Figure 16.3 illustrates one arrangement.
A low-level outlet is provided, fitted with a check valve to prevent
inflow to the tank at low level. The filling connection enters the tank
above TWL, maintaining a piezometric level in the inlet pipeline
sufficient to ensure that the check valve remains closed under normal
flow conditions.
Suppose a pump is tripped at the upstream end of the pipeline caus-
ing piezometric level upstream of the tank to fall and flow to decelerate
and reverse. When head at the filling connection falls below the inlet
level, inflow will cease and if piezometric level continues to decline
until it is below water level in the tank, the check valve will open to
allow flow from the tank back into the pipeline. Hydraulic level at
the downstream end of the pipeline is then essentially controlled by
water level in the tank, thus maintaining positive pressures at this
end of the system. Water from the tank is provided to allow refilling
of any pressure vessels which may be present and also to permit evacu-
ation of possible air pockets through air valves. The volume within the
tank has to be sufficient to fulfil these objectives while maintaining
adequate storage to meet normal operational requirements.
282
Pressure transients in water engineering
The back-flow connection only influences hydraulic transient events
once flow has reversed and has no influence prior to this happening. A
possible downside to this type of arrangement would be if a pipe burst
were to occur in the upstream pipeline. Then there would be nothing
to prevent the discharge chamber emptying. An ideal arrangement
from a hydraulic standpoint would be to have an actuated valve
which opens as necessary to provide any refilling water to the upstream
pipeline. Once the calculated volume had passed through the back-flow
connection, this valve would automatically close.
283
Rising main area = A
Reversed flow connection
with non-return valve (NRV)
Outflow connection
or drawoff
M
Bottom water level (BWL) or
Lowest drawoff level (LDL)
M
Top water level (TWL)
Storage tank surface area = A
t
Piezometric level
while filling
Filling connection
Loss in reversed
flow connection
Piezometric level
during reversed flow
Inlet loss
Fig. 16.3. Low-level back-flow connection
Discharge conditions
16.4 Siphon breakers
Where a submerged discharge to a storage facility exists at the down-
stream end of a pressure pipeline system, it is not uncommon for flow
to pass through a siphon arrangement prior to exiting from the pipeline
system. Measures can be included in the shape of a siphon breaker to
prevent reversed flow from storage. Two examples of such arrangements
are considered.
16.4.1 Above-ground storage tanks
The first of these concerns steel water storage tanks at Al Haiyer in the
UAE (Fig. 16.4). At the downstream end of a pressure pipeline trans-
mission system, vertical inlet lines rise on the outside of each tank turn-
ing through 1808 to descend inside each cylindrical tank with a
submerged discharge. Piezometric levels in the filling connections can
be significantly influenced by the presence or otherwise of vacuum
breaking arrangements. Figure 16.5 shows possible variations in head,
with and without vacuum breakers.
Without a siphon-breaking arrangement and with the inlet pipes
initially fully primed, siphonic action will continue while tank water
level covers the outlet of the filling connection. While the siphon is
operating, the head just upstream of the filling connection will be
that of tank water level inlet loss, depending upon flow direction. If
the siphon is broken at a low tank water level then, depending on
284
Fig. 16.4. Steel tank with high-level filling connection
Pressure transients in water engineering
285
M
Filing connectionOverflow
TWL
M
WL > base of
filling connection
M
BWL
M
TWL
M
WL < breaker
M
BWL
Steel tank – without vacuum breaker
Steel tank – with vacuum breakers
Filling connection
Piezometric level when WL < base
of filling connection (inflow)
Piezometric level when
WL > base of filling connection
Piezometric level when tank
WL < base of filling connection
(outflow or initial filling)
Piezometric level when
WL at TWL
Outflow
Outflow
Overflow
Piezometric level for
WL > breaker level
Piezometric level when tank
WL < breaker (outflow or
during initial filling)
Piezometric level for
WL < breaker level (inflow)
Vacuum
breakers
Fig. 16.5. Hydraulic conditions with and without vacuum breakers
Discharge conditions
inflow rate, piezometric level could rise to the level of water at the top of
the filling connection. During reversed flow, piezometric level will clo-
sely follow that of the tank water level while the siphon is primed. If the
siphon is broken by a low tank water level, piezometric level will rise to
the top of the filling connection and then descend within the vertical
pipe outwith the tank according to the relationship:
A
s
dH=dt ¼ AV ð16:1Þ
If vacuum breakers are included then during inflow the siphon will
be broken at a much higher level when tank water level falls below
the level of the vacuum-breaking arrangement. While the siphon is
operating upstream, head H closely follows tank water level. Once
the siphon has been broken, H will tend to stabilise to some extent.
At low rates of inflow, head may reach the water level at the top of
the filling connection. For higher flow rates, head will also depend on
air inflow rates at the vacuum breaker. On flow reversal with tank
water level above the vacuum breaker then the siphon will operate
and upstream head will follow tank water level. If water level is below
the vacuum breaker, water level will start at the top of the inlet pipe
and descend within the vertical line outside the tank.
16.4.2 Vacuum disconnecting valves
A discharge arrangement which may be found at the end of a treated
effluent pumping main is in the form of a siphon fitted with a
vacuum disconnecting valve (Fig. 16.6). In the system illustrated,
twin submerged outlets discharge to a tailbay or canal figure
(Fig. 16.7). This installation forms one part of the Al Ghouta Irrigation
Project which conveys treated effluent from the City of Damascus
for reuse as irrigation water in rural areas. The vacuum disconnection
valves are closed during forward flow and open when flow reverses.
When pumps are started, the static head which they experience is
dictated by the invert level of the highest point of the pipeline if the
system is fully primed or possibly by some lower water level depending
upon antecedent transient events. In any event, the discharge pipes will
be deprimed down to the tailbay effluent level below the high point con-
taining the vacuum disconnecting valve. On the upstream side of the
high point, effluent level may be at summit invert level or at some
lower elevation.
After pumps are started, air will gradually be purged or ‘scavenged’
from the system with the vacuum disconnecting valve remaining shut
286
Pressure transients in water engineering
287
Fig. 16.6. Siphon outfall with vacuum disconnecting valve
Discharge conditions
288
Fig. 16.7. Siphon discharge to downstream canal
Pressure transients in water engineering
during forward flow. As air is removed, the siphon is finally primed with
piezometric level over the summit, falling to reach tailwater
level þdownstream losses (Fig. 16.8). Sub-atmospheric pressure will
prevail over the summit, thus minimising pumping head.
For a typical pumping system of the Al Ghouta Project, Fig. 16.9
illustrates changing effluent level predicted in the upstream leg of the
discharge siphon. Initially the siphon is fully primed with pumps run-
ning. After pump failure, flow rate decreases and eventually starts to
reverse. On flow reversal over the summit, the vacuum disconnecting
valve opens and the siphon is broken. Under reversed flow, the effluent
level starts to fall, slowly at first and then more steeply as the upstream
leg of the siphon starts to empty in order to supply the liquid necessary
for pressure vessel refilling. When the effluent level reaches the rising
main, piezometric level is largely stabilised for a time by the relatively
flat pipeline profile. When flow becomes positive once more, the
upstream leg of the siphon partially refills. When vessels are filling,
289
M
M
M
Tailwater (canal)
effluent level
Vacuum disconnecting valve
Piezometric level after
vacuum is broken
H
H
H
V +ve
H
Piezometric level during
steady pumping and
with siphon primed
Piezometric level while
upstream limb is
filling or emptying
Rising main
Common horizontal datum
Minimum
piezometric level
Q
Q
u/s
Fig. 16.8. Schematic of siphon with vacuum disconnecting valve
Discharge conditions
the siphon pipes are emptying to provide the vessels with the required
liquid and when the vessels release effluent, piezometric level in the
upstream part of the siphon is recovering.
Effluent level is again determined by the equation:
A
s
dH=dt ¼ AV ð16:1Þ
with A
s
¼ A
u=s
=sinð
u=s
Þ while H soffit of rising main and A
s
¼
A=sinðÞ for H < soffit of rising main. The much shallower gradient
of the rising main usually has a stabilising influence upon water level
and piezometric level.
The effect of this oscillation in head at the siphon end of the system
can be seen in Fig. 16.10 which depicts predicted maximum and mini-
mum hydraulic levels along the rising mains. Initial downsurge after
pumps are tripped takes place while flow in the system is positive.
Along the upstream parts of the pumping mains the minimum down-
surge is developed while discharge head is controlled by the tailwater
level during siphoning. After flow reversal, head at the siphon end of
the system first rises as the vacuum disconnecting valve opens, and
then falls as the upstream limb of the siphon deprimes. Maximum
head towards the downstream end of the system is influenced by the
maximum level as the siphon is broken. As the vessels refill, head
at the downstream end of the system decreases and so peak head at
the pumping station is partly determined by the low downstream
head resulting in a reduced maximum pressure. Minimum head along
290
Elevation (mOD)
Time (min.)
622
621
620
619
618
617
616
0.25 0.5 0.75 1.0 1.25
Water level in
discharge pipework
Upstream
pipework
refilling
Minimum water level
Upstream
pipework
emptying
System primed
Valve opens
Fig. 16.9. Head variation at siphon following pump trip
Pressure transients in water engineering
downstream stretches of the pumping main is also influenced by
emptying of the siphon pipes.
Figure 16.11 shows envelope curves for a different element of the Al
Ghouta Irrigation Scheme. Maximum and minimum head lines have
been extrapolated downstream (dotted line ... ... ...) to show how
the extremes of piezometric level are influenced by prevailing effluent
level at the discharge end of the system.
291
0.25 0.5 0.75 1.0
630
625
620
615
610
Maximum piezometric level
Minimum piezometric level
Chaina
g
e (km)
Elevation (mOD)
Vacuum
breaker valve
Pipeline profile
Pumping
station
Fig. 16.10. Envelope curves following pumping failure
Chaina
g
e (km)
Elevation (mOD)
0.25 0.5 0.75 1.0
Pipeline profile
Vacuum breaker
valve
Minimum transient
hydraulic gradient
Maximum transient
hydraulic gradient
Pressure vessels
at pumping station
630
625
620
615
610
Fig. 16.11. Envelope curves illustrating effect of vacuum breaker valve
Discharge conditions